The 107% rule refers to the time taken to finish a lap. During the first phase of qualifying, drivers have to finish a lap within 107% of the fastest Q1 time. For example, if the fastest drivers in Q1 finished in 100 seconds, then every other car has to turn in less than 107 seconds.
In the 1998 Japanese Grand Prix, Riccardo Rosset turned in 107.234% of the fastest Q1 time. So he wasn’t allowed to start the race. This rule was introduced in 1996. A slow car poses a safety risk to other cars, hence this rule was placed.
However, under special circumstances, stewards may allow a car to start the race. For example, if the car was fast enough during practice but slowed down due to weather or mechanical issues then the team can appeal.